Diffusion,swelling, and consolidation in glassy polystyrene microspheres

The effects of prior thermal and swelling history on the kinetics and apparent equilibria of subsequent n-hexane sorption in monodisperse, submicrometer diameter, glassy polystyrene microspheres were studied. Repetitive sorption and desorption cycling was compared with continuous sorption and desorption experiments. The apparent equilibrium uptake of n-hexane in preswollen samples decreased monotonically with the cumulative time under vacuum independent of the cycle frequency or the number of sorption-desorption cycles. This consolidation was modeled as a first order relaxation process with a single characteristic relaxation time. “As-received” samples swelled in the presence of the penetrant and the apparent equilibrium n-hexane content increased monotonically with the time under n-hexane. The Berens-Hopfenberg diffusion-relaxation model accurately describes the cyclic and continuous swelling behavior of the “as-received” sample. At each temperature studied, a true equilibrium n-hexane content was approached asymptotically for the preswollen and “as-received” samples after sufficient time under vacuum or n-hexane, respectively. Whereas the apparent sorption equilibria were controlled by the cumulative time under vacuum or n-hexane for the preswollen and “as-received” samples, respectively, the absorption kinetics are subject to a systematic variation which depends only on the immediate prior vacuum history of the sample. The temperature dependence of the kinetic and equilibrium parameters describing diffusion, consolidation, and swelling suggests a unified molecular interpretation of these diverse glassy-state transport and relaxation processes.     

Kinetics of vapor and liquid transport in glassy polyblends of polystyrene and poly (2,6-dimethyl 1,4-phenylene oxide) Part II

The kinetics of n-hexane vapor and n-hexane liquid sorption in solution cast films of polystyrene, poly(phenylene oxide), and blends of these homopolymers were studied over a significant range of temperature and penetrant activity. The kinetics of concomitant solvent crazing, apparent at high penetrant activities, were also monitored. In all cases the kinetics of sorption and crazing obeyed predominantly Case II or relaxation-controlled behavior. Although the rates of crazing and sorption at high activities was much more rapid in the homopolymers than in the blends, the sorption rate at lower penetrant activities increased monotonically with increasing poly(phenylene oxide) content. These kinetic results qualitatively superimpose upon the equilibrium relationships reported in Part I of this series. Specifically, at a fixed temperature, the rate of crazing was virtually a unique function of equilibrium n-hexane content independent of polymer composition and largely independent of penetrant activity. The coupling between rate of sorption and equilibrium penetrant content was dramatic. In limiting cases, the sorption rate increased by a factor of 10,000 apparently due to a twofold increase in equilibrium penetrant concentration. This seemingly complicated kinetic behavior is explained rather simply in terms of the equilibrium relationships between organic penetrants and polymeric glasses developed and interpreted in the first part of this series.     

Transport properties of dichloromethane in glassy polymers. II. Amorphous syndiotactic polystyrene films

Sorption and diffusion of dichloromethane vapor were measured in amorphous syndiotactic polystyrene films, obtained with different cooling conditions and after controlled aging times at different temperatures. The diffusional behavior, at the temperature of 25°C, was characterized by three stages, depending on penetrant activity. In the first stage, at low activity, the diffusion coefficient was independent of vapor concentration; the second stage was characterized by concentration-dependent diffusion, whereas in the third stage, at high activity, the strong interaction solvent–polymer increased the mobility, allowing the polymer crystallization. The different cooling conditions neither have an effect on the diffusional behavior nor on the sorption curve. The aging, both at room temperature and at 70°C, did not change the diffusion parameters, but led to the appearance of more and more anomalous sorption behavior. The sorption curve, as a function of vapor activity, did not show any difference for the fresh and the aged-at-room temperature samples, whereas the samples aged at 70°C presented a lower sorption at low activity. The presence of ordered domains, impermeable to the penetrant at low activity, was suggested on the basis of sorption results. The solvent-induced crystallization was investigated for all the samples. Crystallization was induced at an activity of 0.45 for the fresh and the aged-at-room temperature samples; at variance, the samples aged at 70°C crystallize at a slightly higher activity, reaching, nevertheless, a higher level of crystallinity. © 1993 John Wiley & Sons, Inc.     

Errors associated with swelling in the analysis of polymer-solvent diffusion measurements

Sorption curves are generated from a mathematical model which includes the influence of the polymer swelling for unsteady-state sorption of a vapor or liquid by a polymer. To investigate the simultaneous effects of the specific volumes of the polymer-penetrant pair and the difference between the final and initial equilibrium concentrations on the sorption curves, statistical experimental design approach is used. Simulation results obtained from the numerical solution of model equations are utilized to estimate the error that would occur if one simply evaluates the diffusion coefficient using the traditional formulas derived from the analytical solution of the sorption equation. An empirical expression is developed that describes the effects of the difference between the final and initial equilibrium concentrations and the specific volumes of the polymer and the penetrant on the magnitude of error in diffusivity associated with the use of one of these traditional formulas so called the initial slope method. The predictive ability of the regression model is tested by performing additional simulations not used in the regression analysis.     

The effect of sorbed penetrants on the aging of previously dilated glassy polymer powders. I. Lower alcohol and water sorption in poly(methyl methacrylate)

Sorption kinetics and equilibria for methanol, ethanol, and n-propanol in 0.544 μm diameter poly(methyl methacrylate) microspheres were determined at 35°C over a wide range of relative pressures. Sorption isotherms were concave to the pressure axis at low relative pressures and convex to the pressure axis at higher relative pressures. These results, considered in the context of recently reported data for high pressure sorption of gases in polymeric glasses, suggest that the S-shaped isotherms reported here are examples of a generalized isotherm which describes sorption behavior of all penetrants in glassy polymers if an appropriate range of concentration is traversed by the experimental protocol. The effects of dialating the microspheres by preswelling with methanol were studied by subsequent low pressure sorption of water, methanol, ethanol, and n-propanol at 35°C. The preswollen microspheres exhibited initially higher sorption capacities than the as-Received samples, but tended to consolidate with time following the preswelling treatment. The aging process, monitored by periodic short-term sorption with the various penetrant probes, was arrested by contacting the microspheres with an activity of n-propanol sufficient to maintain a sorbed concentration of approximately 1 wt %. The aging was significantly retarded by the presence of low concentrations of water and ethanol. Conversely, the aging process appeared to be essentially unaffected by the presence of correspondingly low concentrations of methanol. The complex kinetics describing the sorption of the various penetrants ranged from Fickian diffusion to polymer relaxation-controlled absorption, depending upon penetrant, relative pressure, and prior exposure history. The low temperature preswelling of the microspheres markedly increased the rate of sorption as well as the respective apparent equilibrium sorption.     

The effect of sorbed penetrants on the aging of previously dilated glassy polymer powders. IV

Uniform, submicron-diameter polystyrene (PS) and poly(methylmethacrylate) (PMMA) microspheres were dilated by preswelling with pure organic vapors followed by rapid removal of the preswelling penetrant by protracted evacuation of the preswelling chamber to a pressure of 10^?3 mm Hg. Aging of the preswollen polymers was carried out both in vacuum and in the presence of various penetrants at sorbed concentrations typically less than 2 wt%. Inferences about relaxations of the polymers were based upon changes in concentrations of the penetrants within the microspheres, at a given temperature and penetrant activity, which result from aging in vacuum or in the presence of penetrant. The kinetics of the relaxations were monitored by probing the expanded glasses with relatively low concentrations of penetrants. In general, the continuous presence of these low concentrations of probe molecules either arrested or retarded the ensuing relaxation as compared with the aging that occurred in vacuum. A series of lower monohydric alcohols, lower n-alkanes, and some other similar penetrants were used as probes to test explicitly and systematically the effects of size and structure of the penetrant contacting the polymer during aging on the decay of excess sorption capacity of the preswollen glassy polymers. Decay of excess sorption in the presence of penetrant was evident only when molecularly small penetrants with interactive functional groups, alcohols for example, were sorbed into preswollen PMMA. This result suggested that the relaxation occurring in the presence of penetrant involved specific interactions between the penetrants and the carbonyl groups in the PMMA.     

Sorption/desorption properties of ethanol,toluene, and xylene in poly(dimethylsiloxane) membranes

Sorption/desorption kinetics and sorption equilibria have been determined for ethanol, toluene, and xylene vapors in a poly(dimethylsiloxane) membrane containing about 32 wt % silica resin at 25°C. Dependence of diffusion coefficient on vapor activity and sorption isotherms have been compared to identify the transport mechanisms of those penetrants in the PDMS membrane. The analysis of Zimm–Lundberg clustering functions showed that all three penetrants had a tendency to form clusters and ethanol molecules might be immobilized by the residual silanol groups within the silica resin in the membrane. The diffusion coefficient of toluene was roughly constant and that of xylene slightly decreased as increasing the vapor activity due to the competing effects of penetrant clustering and solvent swelling of polymer. The diffusion coefficient of ethanol versus activity exhibited a maximum due to the effects of ethanol immobilization and cluster formation. The freevolume effect by solvent swelling to diffusion was obscured by either penetrant clustering or immobilization for the three penetrant–polymer systems. © 1994 John Wiley & Sons, Inc.     

Vapor and liquid equilibria in glassy polyblends of polystyrene and poly(2,6-dimethyl-1,4-phenylene oxide) Part I

The equilibrium sorption of n-hexane vapor and n-hexane liquid in solution cast films of polystyrene, poly(phenylene oxide), and blends of these homopolymers was studied over a significant range of penetrant activity and temperature. These equilibrium sorption measurements were supplemented by density determinations, refractive index measurements, differential scanning calorimetry and differential thermal analysis. A seemingly complicated pattern of results emerged when the equilibrium penetrant content was plotted as a function of blend composition. At relatively low activity and temperature the equilibrium concentration of n-hexane in these films monotonically increased with poly(phenylene oxide) content in the blend. Conversely, at high activities and in unit activity liquid, the equilibrium penetrant concentration exhibited a distinct minimum when plotted as a function of blend composition. At higher activities, solvent induced crazing accompanied the sorption of penetrant. These results were explained consistently by considering the nature of the sorption isotherm over an activity range sufficient to lower the glass transition temperature, of the equilibrated and swollen blend, below the temperature of the sorption experiment. Most importantly, the interpretation and explanation of these data are based upon phenomena common to all glassy polymer-organic penetrant systems and no special properties of this blend system were included in the analysis. The results, therefore, reflect the apparent homogeneity of polystyrene-poly (phenylene oxide) blends and are useful in considering the equilibrium of penetrant sorption in glassy polymers as a general class of materials.     

Characterization of glassy state relaxations by low pressure carbon dioxide sorption in poly(methyl methacrylate)

Poly(methyl methacrylate) (PMMA) microspheres were swollen in methanol vapor, the swelling penetrant was quickly evacuated, and the subsequent relaxation of the polymer under vacuum was monitored by determination of the rate of settling of rapidly measured low pressure pseudoequilibrium CO₂ sorption isotherms. The decrease in CO₂ sorption capacity occurred very rapidly at short times, but the final stages of consolidation were protracted. In all cases, the microspheres were under vacuum between isotherm determinations. A single relaxation time is not sufficient to describe the relaxation processes characterized by the time-dependent sorption measurements. The sorption relaxation curves are similar in shape to volume relaxation curves for glassy polymers following imposition of a large pressure or temperature step change. The observed similarity between the sorption relaxation curves and classical volume relaxation curves is consistent with the notion that the excess sorption capacity introduced by methanol preswelling results from excess unrelaxed volume introduced into the glass by the quickly removed alcohol. As the excess volume relaxes, the excess sorption capacity decreases. One can, therefore, monitor the subtle process of consolidation using CO₂ as a probe of the excess volume introduced by the swelling perturbation. Subatmospheric pressure CO₂ sorption isotherms measured between 20 and 40°C for two different diameter microsphere samples (5436 Å and 1453 Å) for pressures up to 700 mm Hg were concave to the pressure axis. Such general isotherm shapes can be described by a two-term expression consisting of a Henry's law term and a Langmuir term. The Langmuir term, which arises due to unrelaxed volume in the nonequilibrium glass, is responsible for the observed concavity in the sorption isotherm. Annealing the sample, increasing the temperature of the sorption experiment closer to the T_g of the PMMA or permitting the preswollen sample to relax tends to reduce the concavity of the isotherm relative to the corresponding case for sorption in the preswollen sample measured at 25°C. This trend is presumably a consequence of the reduction in unrelaxed volume in the glass which attends either annealing, approaching the glass transition temperature of the polymer, or consolidation of excess volume following exposure to a swelling penetrant.     

Evidence of dual mobility in sulfur dioxide-polyarylate system: An integral sorption analysis

Integral sorption/desorption measurements were carried out for the sulfur dioxide-glassy polyarylate polymer system at 25°C, 40°C, 55°C, and 63°C. The transport of sulfur dioxide in the glassy polyarylate polymer was governed by Fickian diffusion. The effective diffusion coefficient of sulfur dioxide increased with increasing penetrant concentration. The concentration dependence of the effective diffusion coefficient is explained on the basis of the partial-immobilization model developed by Paul and Koros. The mobility of the molecules sorbed in the Langmuir mode is shown to be significantly lower than the mobility of the molecules in Henry's law dissolution mode. The predictions of permeability values as a function of upstream gas pressure are presented. The equilibrium sorption isotherms for this system are well represented by the dualmode sorption model. The eltergetics and the temperature dependence of the dual-mode parameters are also discussed.     

Anomalous sorption kinetics in the methanol vapor–poly(methyl methacrylate) system

The non‐Fickian sorption kinetics of methanol vapor in poly(methyl methacrylate) films 8 and 51 μm thick at 25°C are presented. The behavior of the system was studied in series of interval and integral absorption runs. The relevant diffusion coefficient and viscous relaxation processes were studied separately by kinetic analysis of the first and second stages of sorption kinetic curves. The sorption isotherm concaved upward at high activities, this being typical of Flory–Huggins behavior, whereas it exhibited a convex‐upward curvature at low methanol vapor activities, this indicating sorption in the excess free volume of the polymer matrix. After excess free‐volume fill‐up, the concentration dependence of the diffusion coefficient was found to be well represented by the free‐volume theory of Vrentas and Duda. Relaxation frequencies calculated from the second stage of two‐stage curves exhibited a weak dependence on the concentration. Integral sorption experiments indicated that the system exhibited nearly case II kinetics at high methanol vapor activities. © 2005 Wiley Periodicals, Inc. J Appl Polym Sci 97: 1184–1195, 2005     

Integral sorption with induced crystallization

We studied the integral sorption of saturated, organic vapors in amorphous films of poly (ethylene terephthalate) (PET) using a spring balance apparatus. The penetrants employed (methylene chloride [MeCl₂] and N. N. dimethyl formamide [DMF]) induce substantial crystallization of the polymer during sorption. The experimental data (mass of vapor absorbed versus exposure time) do not obey Fick's law for diffusion but reflect the influence of time dependent polymer swelling and crystallization. The data show that polymer swelling controls the penetrant transport in thin films, while molecular diffusion in the highly swollen semi-crystalline polymer controls in thick films. Small activation energies were found for transport in thin films suggesting that ductile deformation controls the swelling in PET. A mathematical model developed previously explains the important features of the experiments.     

Coupling between mass diffusion and film temperature evolution in gravimetric experiments

In gravimetric experiments, the swelling and the drying of polymer films is used to investigate the thermodynamic properties and the mutual diffusion coefficient of polymer/solvent systems. Usually thermodynamic equilibrium at the interface between the film and the solvent vapor and thermal equilibrium between the film and the surroundings are assumed. In this paper we show that the second assumption may fail. Indeed, during a swelling or drying experiment, the temperature of the film surface changes due to the latent heat of vaporization, which induces a variation of the activity. When the corresponding variation of the solvent content is of the same order than the variation due to the sorption experiment and when the thermal time constant is significant compared to the characteristic mass diffusion time, this thermal effect must be taken into account when analyzing sorption data. We evaluate the consequence of this thermal effect on gravimetric experiments and develop a complete model to take this phenomenon into account when analyzing sorption data. As an example, the mutual diffusion coefficient for the system PIB (polyisobutylene)/toluene is estimated for various solvent concentrations at 25 °C.     

溶剂在高分子膜中传递现象研究的进展

溶剂在高分子膜中吸收和解吸的传递机理非常复杂,对其传递过程的研究有助于膜分离过程的开发、膜材料的选择。本文对溶剂在高分子膜中传递现象研究的进展作简要介绍。     

Transport properties of dichloromethane in glassy polymers. I. Atactic polystyrene films

Sorption and diffusion of dichloromethane vapor were measured in atactic polystyrene films, obtained with different cooling conditions and after controlled aging times at different temperatures. The diffusional behavior is characterized by three zones, depending on temperature and penetrant activity. In Zone I, at low activity, the diffusion coefficient is independent of vapor concentration; Zone II is characterized by concentration-dependent diffusion, whereas in Zone III structural transformations are possible. The study of diffusion at three temperatures allowed building of a temperature-penetrant concentration diagram, which is very useful to visualize the different zones of behavior. The aging at room temperature has no effect on the curve of sorption as a function of vapor activity, whereas it determines two effects on the diffusion: a decrease of the zero concentration diffusion coefficient and a more and more anomalous behavior with the aging time. The aging at 70°C produces the same effects on the diffusion behavior as the aging at room temperature; in addition, a decrease sorption is observed at low penetrant activity. The possible presence of ordered domains, impermeable to the vapor, in the samples stored at 70°C, was suggested on the basis of sorption results.     

Water and water vapor sorption studies in polypropylene–zeolite composites

Water and water vapor sorption to porous polypropylene–zeolite composites prepared by hot pressing have been studied as a function of zeolite loading. This work presents the first report on the effect of the zeolite as a filler on the water‐sorption properties of PP composites. Water swelling experiments were conducted at 25°C using pure PP and PP–zeolite films samples having different zeolite loadings (6–40 wt %). Because PP is a hydrophobic polymer, it does not sorp any water, but the composites having 10, 20, 30, and 40% zeolites have sorbed 0.63, 1.00, 1.72 and 3.74% water, respectively. The zeolite itself at the same conditions sorbed 24.5% water. As the filler loading in the composites increased, equilibrium uptake values increased also. On the other hand, water vapor sorption and kinetics has been studied using a Cahn 2000 gravimetric sorption system. Within in the range of 0.35–0.95% water vapor was adsorbed by the composites containing 10–40 wt % zeolites. Experimental effective water vapor diffusivities of the composite films was about one order of magnitude higher (10‐fold) than the experimental water diffusion coefficient in composites. The transport of water in composites was slower than that in the liquid water due to the longer diffusion pathway and adsorption on the surface of the composites. Although the liquid water may fill all the voids in the composite, water vapor is adsorbed on the surface of the zeolite only. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 90: 3069–3075, 2003     

Sorption,desorption, resorption,redesorption, and diffusion of haloalkanes into polymeric blend of ethylene–propylene random copolymer and isotactic polypropylene

Molecular transport of haloalkanes into sheets of a polymeric blend of an ethylene–propylene random copolymer and isotactic polypropylene has been studied by a sorption gravimetric technique in the temperature interval of 25–70°C. For all liquids, equilibrium sorption, desorption, resorption, redesorption, and degree of penetrant overshoot have been influenced by the nature of the liquid and the temperature. Diffusion coefficients were calculated from the sorption–desorption kinetic curves using Fick's mathematical relations. The values of diffusion coefficients followed the Arrhenius-type behavior. The temperature-dependent sorption data were analyzed using the van't Hoff relation. The activation parameters for diffusion and heat of sorption data were discussed in terms of the molecular interactions between liquids and the polymer chain segments. The experimental and calculated results are discussed on the basis of the chemical nature of liquids. © 1995 John Wiley & Sons, Inc.     

Time and temperature dependent sorption in poly-ether-ether-ketone (PEEK)

The possible multimodal sorption mechanisms in glassy amorphous poly-ether-ether-ketone (PEEK) are presented. By varying the penetrant-polymer affinity, experimental temperature, and external solvent activity, a broad range of sorption behaviors from ideal Fickian diffusion to limiting relaxation controlled kinetics is observed. In particular, water, methylene chloride, and n-heptane sorption kinetics are analyzed and interpreted on the basis of the multiple transport mechanisms. Low uptake liquid n-heptane sorption follows ordinary Fickian diffusion. Analogously, water vapor at low activity, is sorbed in small amounts in the same limiting mode while, at higher activities, the moderately higher penetrant uptakes induce slow relaxation coupled with ideal Fickian diffusion. The highly interacting methylene chloride leads to ideal Fickian diffusion only at very low activities, while anomalous non-ideal Fickian diffusion and limiting Case II and diffusion controlled swelling are observed at moderate and at high solvent activities, respectively. Limiting Case II sorption of methylene chloride in PEEK has been observed only at a very low temperature (?32°C). The optical microscopy observations of cryogenically fractured samples contacted with liquid methylene chloride at 5, 20 and 36°C revealed the presence of a sharp front moving linearly with the square root of time. Solvent induced crystallization in methylene chloride swollen samples was detected by means of differential scanning calorimetry (DSC) and wide angle X-ray scattering (WAXS). Finally, sorption from liquid methylene chloride/n-heptane solutions with varying compositions are presented. The progressive increase of the more high sorbing methylene chloride concentration in the solutions, leads to the same wide variety of sorption behavior observed in the methylene chloride vapor sorptions. The gas chromatographic (GC) analysis indicated that the presence of methylene chloride enhanced the n-heptane sorption in the polymer.     

Sorption and transport of linear and branched ketones in biaxially oriented polyethylene terephthalate

Equilibrium sorption and kinetics of acetone, methyl ethyl ketone (MEK), methyl n-propyl ketone (MnPK), and methyl i-propyl ketone (MiPK) uptake in uniform, biaxially oriented, semicrystalline polyethylene terephthalate films were determined at 35 °C and low penetrant activity. Sorption isotherms for all penetrants were well described by the dual-mode sorption model. Sorption and desorption kinetics were described either by Fickian diffusion or a two-stage model incorporating Fickian diffusion at short times and protracted polymer structural relaxation at long times. Diffusion coefficients and equilibrium solubility at fixed relative pressure decreased in the following order: acetone>MEK>MnPK>MiPK. Diffusion coefficients for each penetrant increased with increasing penetrant concentration.